Anisotropy of electron-phonon interactions in alkali metals

Electron-phonon scattering in the solid alkalis is distinguished from that in most other metals by a combination of three circumstances: The phonon spectra and structure factors are very anisotropic, the Fermi surface in the reduced zone is simply connected and virtually spherical and important large momentum transfers (0.7<(q/2k _F)<1.0) fall within the first large peaks of the phonon structure factors. Anisotropy of microscopic contributions to the macroscopic coefficients is controlled by and is quite sensitive to values of electron-ion matrix elements at large momentum transfer, and can be explored by a realistic yet relatively simple theoretical calculation. A brief summary is presented of such calculations, for the all alkalies, of mean free paths, thermoelectric powers, and electron-phonon mass enhancements. The results show marked anisotropy only for lithium, are consonant with experimental low field Hall coefficients and in addition indicate strong anisotropy in the mass enhancement for lithium.     

Anisotropic electron-phonon scattering in metals

A previously published general theory for the effects of electron-phonon scattering in metals involves all relevant anisotropies and permits a virtually exact solution of the Boltzmann equation. The electron-phonon interaction is represented by a few Wannier matrix elements that are adjusted to experimental data. Calculations of the electron lifetime and the mass enhancement in copper show good average agreement with the experiments. For reproducing the exact anisotropies further non-diagonal elements have to be considered. The calculated temperature dependence of the Hall effect agrees qualitatively with the observations and reveals the local maximum found for both pure copper and dilute alloys.     

Anisotropic electron-phonon scattering in metals

A previously published general theory for the effects of electron-phonon scattering in metals involves all relevant anisotropies and permits a virtually exact solution of the Boltzmann equation. The electron-phonon interaction is represented by a few Wannier matrix elements that are adjusted to experimental data. Calculations of the electron lifetime and the mass enhancement in copper show good average agreement with the experiments. For reproducing the exact anisotropies further non-diagonal elements have to be considered. The calculated temperature dependence of the Hall effect agrees qualitatively with the observations and reveals the local maximum found for both pure copper and dilute alloys.     

Electron Raman scattering in metals with strong electron-phonon coupling

Inelastic light scattering by the carriers interacting with phonons in the anisotropic metals with large penetration depth is theoretically studied. It is shown that the strong temperature dependence of the Raman scattering intensity in the region of phonon frequencies is the main characteristic feature of these processes. The effects of anisotropy, impurities and the strength of electron-phonon interaction on the frequency and temperature dependences of the polarization operator are analysed. Taking into account the anisotropy vertex corrections which obey a system of the Boltzman-type integral equations should leads to the considerable changes of the frequency behavior of scattering cross section for low frequencies. However, the changes of the temperature dependence are not so drastic. Increasing the electron-phonon coupling constant affects the particle-hole polarization operator in two possible ways to weaken temperature dependence and to make flatter frequency curves. The same effects are also from impurities. Some theoretical consequences which concern the role of electron-phonon interaction for electron Raman scattering in high-T _c superconductors aboveT _c are proposed.     

Experimental and theoretical study of the electron-phonon scattering rate in potassium

Limiting-point radio-frequency size effect measurements have been performed in potassium to measure the anisotropy and magnitude of the electron-phonon scattering rate. The anisotropy is too small to be resolved by the method, and is estimated to be less than 10 per cent at low temperatures. Theoretical calculations confirm the small anisotropy, but yield a rate at least 40 per cent larger than that observed.     

Ultrasonic determination of electron-phonon scattering rates in copper

Electron-phonon scattering rates in ultrapure single crystals of copper have been determined from the temperature dependence of the magnetoacoustic oscillation amplitudes for various orbits on the Fermi surface using both longitudinal and transverse waves. The central belly orbit seattering rate is found to be (6.0±0.3)×10⁶ T ³ sec^?1. Additionally, a rate of (2.9±0.2)×10⁶ T ³ sec^?1 is found which is attributed to belly orbits displaced from the zone center by about 1.25/a ₀, wherea ₀ is the lattice constant. Geometric oscillations associated with the [111]—directed open orbit are observed at low fields forq‖ [113] and the rate for this orbit is found to be (4.8±0.3)×10⁶ T ³ sec^?1. Geometric oscillations for the dog's bone and neck orbits are observable but rates for these orbits are believed to be unreliable. Our measured rates are compared with those of other workers.     

Ultrasonic determination of electron-phonon scattering rates in copper

Electron-phonon scattering rates in ultrapure single crystals of copper have been determined from the temperature dependence of the magnetoacoustic oscillation amplitudes for various orbits on the Fermi surface using both longitudinal and transverse waves. The central belly orbit seattering rate is found to be (6.0±0.3)×10⁶ T ³ sec^–1. Additionally, a rate of (2.9±0.2)×10⁶ T ³ sec^–1 is found which is attributed to belly orbits displaced from the zone center by about 1.25/a ₀, wherea ₀ is the lattice constant. Geometric oscillations associated with the [111]—directed open orbit are observed at low fields forq [113] and the rate for this orbit is found to be (4.8±0.3)×10⁶ T ³ sec^–1. Geometric oscillations for the dog's bone and neck orbits are observable but rates for these orbits are believed to be unreliable. Our measured rates are compared with those of other workers.     

The electron-phonon coupling constant of amorphous metals

The Eliashberg function and the electron-phonon coupling constant fora-Ga are calculated in the framework of the free-electron model, using measured sound velocities and resistivity data for the normal state. In particular, the contribution of the soft transverse acoustic phonons is estimated. For phonon frequencies up to 300 GHz, it amounts to not more than 5% of the total coupling constant.     

Optical sum rule in metals with strong electron-phonon interaction

The properties of a superconductor featuring strong electron-phonon and electron-impurity interactions have been studied in a single-band approximation. It is shown that the elastic scattering of electrons on static impurities decreases the electron-phonon interaction constant in proportion to the ratio of the electron-impurity relaxation rate and the seeding band width. The optical spectral weight (integral of the real part of the optical conductivity) in various energy intervals of a metal in the normal and superconducting states has been calculated as a function of the temperature and the superconducting gap. In the region of large (compared to the phonon) energies, the dependence of the spectral weight on the superconducting gap is weak, while the dependence on the temperature is completely determined by the corresponding dependence of the relaxation rate due to the elastic electron-phonon scattering far from the Fermi surface. It is shown that a difference in behavior of the spectral weight between the normal and superconducting states at lower energies is determined by so-called Holstein’s shift of the feature in the optical conductivity spectrum (rather than by the gap width, as it is commonly believed) and sharply decreases upon the introduction of impurities.     

Anisotropy of the electrical resistance of ferromagnetic metals

The spin-orbital mechanism of electron scattering in 3-d-ferromagnetic metals is reviewed on the basis of the two-zone model. It is shown that in the case of free s-electrons and strongly bound d-electrons it is the latter which have the predominant role in the anisotropy of the electrical resistance. It is indicated that to produce quantitative agreement with experiment account must be taken of the deviation of the s-electron wave functions from plane waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 7–12, July, 1972.     

Influence of the inelastic electron-phonon scattering on the superconducting surface resistance

Experimental investigations of the rf losses in superconductors show deviations from the predictions of the weak-coupling theory. In order to explain the observations one has to take into account a number of mechanisms neglected in the weak coupling theory. One of these is the finite lifetime of the electrons due to their interaction with thermally excited phonons described by the strong-coupling theory. We have developed a computer program which calculates the surface impedance of strong-coupling superconductors at finite temperatures. In this paper the main features of the program and numerical calculations of the surface resistance of Sn, Pb, Nb and amorphous Ga are presented.     

Anisotropy of the resistivity of normal hexagonal metals

Using the Mannari-Ziman-Baym theory we calculate the anisotropy in phonon scattering resistivity of normal hexagonal metals. We use a Born von Karman force constant fit to inelastic neutron and X-ray scattering experiments and both empirical and model form factors. U and N processes are explicitly separated. We get reasonable results for the anisotropy of Mg, Cd and Zn but not for Be.     

Effect of electron-phonon scattering on shot noise in nanoscale junctions

We investigate the effect of electron-phonon inelastic scattering on shot noise in nanoscale junctions in the regime of quasiballistic transport. We predict that when the local thermal energy of the junction is larger than its lowest vibrational mode energy eV(c), the inelastic contribution to shot noise (conductance) increases (decreases) with bias as V (sqrt[V]). The corresponding Fano factor thus increases as sqrt[V]. We also show that the inelastic contribution to the Fano factor saturates with increasing thermal current exchanged between the junction and the bulk electrodes to a value which, for V > V(c), is independent of bias. These predictions can be readily tested experimentally.     

Point-contact spectra and electron-phonon interaction functions of platinum metals

The results of the experimental studies of the electron-phonon interaction (EPI) of all platinum metals by point-contact (PC) spectroscopy are reported. The EPI spectral functions are determined using the microscopic theory of PC background. Averaged phonon frequencies are obtained.     

Excitation of nonlinear impurity electron-phonon oscillations. Raman scattering

The impurity is shown to transit into the state of non-linear electron-phonon oscillation upon the passage of a resonance electromagnetic wave pulse. In this case some lines appear in the Raman spectrum at frequencies characteristic for the oscillations.